{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 市场风险\n",
    "市场风险管理，遵循风险识别、风险计量和风险管理三部曲。其中，量化市场风险，是最核心内容。因此设计合适的风险测量指标与方法成为首要任务。\n",
    "在市场中，可以观察到价格波动对资产价值的影响，因此从资产价格变动出发，首先建立第一个概念——收益/损失（Profit/Loss）。\n",
    "## Profit/Loss\n",
    "P/L, 资产的价值变动，准备的定义是在资产在t时点的价值加上期间收益，减去t-1时点价值。\n",
    "\n",
    "$$P/L_t = P_t + D_t - P_{t-1}$$\n",
    "\n",
    "注：\n",
    "1. 如果t与t-1的间隔时间（holding period）长，要考虑时间价值。使用现值（PV）或者终值（FV）来计算。\n",
    "2. 收益和损失互为相反数，即 Profit/Loss = - Loss/Profit。\n",
    "收益/损失（Profit/Loss）是一个绝对量，因此建立了一个衡量收益的相对量，收益率（rate of return)。收益率的计算，有两种定义（方法），算术收益率$r_t$（arithmetic return）和几何收益率$R_t$（geometric return）。\n",
    "\n",
    "$$r_t = \\frac{P/L_t}{P_{t-1}}=\\frac{P_t+D_t-P_{t-1}}{P_{t-1}}=\\frac{P_t+D_t}{P_{t-1}} - 1$$\n",
    "\n",
    "$$R_t=\\ln\\frac{P_t+D_t}{P_{t-1}}=\\ln(1+r_t)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 读入data文件夹里的文件VaRExample.csv，分别计算观察道琼斯指数的算术和几何收益。\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Profit/Loss of DJIA is: \n",
      " Day\n",
      "1      -45.79\n",
      "2      -97.41\n",
      "3       48.19\n",
      "4      -36.35\n",
      "5        9.85\n",
      "        ...  \n",
      "496    410.03\n",
      "497    368.75\n",
      "498   -372.75\n",
      "499   -190.52\n",
      "500    196.89\n",
      "Name: DJIA, Length: 500, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_csv('./data/VaRExample.csv', index_col='Day')\n",
    "djia = df['DJIA']\n",
    "profit = (djia - djia.shift(1)).dropna()\n",
    "print(\"The Profit/Loss of DJIA is: \\n\", profit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Day'>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "profit.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Frequency'>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "profit.plot.hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "profit.plot.kde()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    500.000000\n",
       "mean      -0.394640\n",
       "std      137.235333\n",
       "min     -565.690000\n",
       "25%      -51.872500\n",
       "50%        8.025000\n",
       "75%       68.272500\n",
       "max      432.940000\n",
       "Name: DJIA, dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "profit.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Day\n",
       "1     -0.004081\n",
       "2     -0.008718\n",
       "3      0.004351\n",
       "4     -0.003268\n",
       "5      0.000888\n",
       "         ...   \n",
       "496    0.038647\n",
       "497    0.033463\n",
       "498   -0.032731\n",
       "499   -0.017295\n",
       "500    0.018188\n",
       "Name: DJIA, Length: 500, dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# arithmetic return\n",
    "r = (profit/djia.shift(1)).dropna()\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Day\n",
       "1     -0.004090\n",
       "2     -0.008756\n",
       "3      0.004341\n",
       "4     -0.003273\n",
       "5      0.000888\n",
       "         ...   \n",
       "496    0.037919\n",
       "497    0.032915\n",
       "498   -0.033278\n",
       "499   -0.017447\n",
       "500    0.018025\n",
       "Name: DJIA, Length: 500, dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# geometric return\n",
    "# 根据定义\n",
    "R = (np.log(djia/djia.shift(1))).dropna()\n",
    "R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Day\n",
       "1     -0.004090\n",
       "2     -0.008756\n",
       "3      0.004341\n",
       "4     -0.003273\n",
       "5      0.000888\n",
       "         ...   \n",
       "496    0.037919\n",
       "497    0.032915\n",
       "498   -0.033278\n",
       "499   -0.017447\n",
       "500    0.018025\n",
       "Name: DJIA, Length: 500, dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 根据算术和几何收益之间的数量关系\n",
    "R = np.log(1+r)\n",
    "R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Arithmetirc Return')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Geometric and arithmetric returns\n",
    "x = np.linspace(0, 0.5, 50)\n",
    "y = np.log(1+x)\n",
    "plt.plot(x, y)\n",
    "plt.ylabel('Geometric Return')\n",
    "plt.xlabel('Arithmetirc Return')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating\n",
    "根据观察计算出P/L后，设计合理风险测度的指标，例如VaR和ES，使用参数或非参数方法估计。\n",
    "### 历史模拟法\n",
    "直接使用P/L数据，排序后数分位数。\n",
    "### 半参数法\n",
    "* Age-weighted HS\n",
    "* Volatility-weighted HS\n",
    "* Correlation-weighted HS\n",
    "* Filter HS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% VaR = 243.85\n"
     ]
    }
   ],
   "source": [
    "VaR95 = -profit.quantile(q=0.05,interpolation='higher')\n",
    "print('95% VaR =', np.around(VaR95,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% VaR = 243.85\n"
     ]
    }
   ],
   "source": [
    "# 或者采用 （1-alpha)*n + 1 来计算\n",
    "print('95% VaR =', np.around(-profit.sort_values().iloc[(25)],4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Age-weighted Historical Simulation:\n",
      "95% VaR = 372.75\n"
     ]
    }
   ],
   "source": [
    "# Age-weighted Historical Simulation\n",
    "# Weight the probabiltiy of P/L to discount the older observatations in favour of newer ones.\n",
    "l = 0.94\n",
    "alpha = 0.05\n",
    "n = profit.shape[0]\n",
    "age_weight = np.power(l,np.arange(n,0,step=-1)-1)*(1-l)/(1-np.power(l, n))\n",
    "loss = -profit.sort_values()\n",
    "q = np.sum(age_weight[loss.index-1].cumsum()<=alpha)\n",
    "print(\"Age-weighted Historical Simulation:\")\n",
    "print('95% VaR =', np.around(loss.iloc[q],2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YkWQxFnIcODzAO1dWJuyY48fyK/jFT9GO6tkEJO5/gEjAWroHGR4LsSCB0ydoLL8kSrQt/jLgNTN7HhiKbHTOvceXqkQCtvdQP0Bigz8ybYNO8IrPog3+W/0sQiTZ7O9IfPCX5meRlZ5Gk8byi8+iCn7n3NNmthBY5px7wszyAM0dK7PWvo5+0tPM1yUXJzIzDemUhIh2rp5PAPcDd3mb5gO/9KkmkcDt6+hnfnEuGenRngaLj8o5ObqIS3wX7bv6BuBcoBvAObcDmOdXUSJB29vRn9Bunoiq4hwtui6+izb4h5xzw5E73kVcGtops9b+jv5AFkSpKcmlqXOQ0bFQwo8tqSPa4H/azD5PeNH1i4CfAQ/7V5ZIcHoGR+joGw6kxV9TksdoyGlBFvFVtMF/M9AGbAT+B/Ao8EW/ihIJUmQo56K5iQ/+2pLwMfd3qLtH/BPtqJ6Qmf0S+KVzrs3fkkSCtautF4Al8woSfuzI3EAHDvcDcxN+fEkNJ2zxW9itZtYObAO2eatvfSkx5Ykk3q7WXtIMFgbQ4q8qyiXNYP9htfjFPyfr6vkM4dE8ZzrnSp1zpcDZwLlm9hnfqxMJwK62PhaU5pGdkfhLVbIy0qick8MB7wIyET+cLPg/DFzjnNsd2eCcawCuBf7Sz8JEgrKrrZcl5Ynv5omoKc1j/2EFv/jnZMGf6Zxrn7jR6+fPPNETzazWzJ40s9fMbLOZ3ehtLzWzx81sh/e9JPbyReJrLOTY3d7H4vL8wGqoLcnjgLp6xEcnC/7hGB8DGAX+1jl3GvAm4AYzO43wCKG1zrllwFrvvkhSONg5wNBoKNAWf21pLs3dgwyNjp18Z5EYnGxUz2oz655kuwEnnMTEOdcENHm3e8xsC+GpHq4A3uHtdi/wFPC56EsW8c/OAEf0RNSU5OEcHOwcpK4suL88ZPY6YfA75+JydsvMFgFrgHVAhfehANAMVBznOdcD1wMsWLAgHmWInNT25h4AlgUY/LUl4SGd+zv6FfziC99noDKzAuDnwN84517314O3otekUz845+52ztU75+rLy8v9LlMEgK3NPVQV5VCclxVYDZGpItTPL37xNfjNLJNw6P+3c+4Bb3OLmVV5j1cBrX7WIDIVW5q6WVFZGGgNFXNyyEw3jewR3/gW/GZmwPeBLc65b4x76CHgOu/2dcCDftUgMhXDoyF2tfWyIoELrE8mvA5ALvs0ll98Eu0KXLE4l/B1ABvN7BVv2+eB24GfmtnHgb3An/tYg0jUdrX1MjLmAm/xAyyam8/eQ31BlyGzlG/B75z7PeHRP5O5wK/jisRqa3P4FNSpAbf4AerK8lm/pwPnHOE/nkXiJ7HLC4kksS1NPWSlpyXFSJrF5fn0DY/R1jMUdCkyCyn4RTwbDnRyavUcMhO83OJkIh8+De3q7pH4C/4dLpIExkKOjQe6WF1TFHQpwNHg363gFx8o+EUIn9jtGx5jdU1x0KUAUF2US1ZGmoJffKHgFwFe2d8JwOra4kDriEhLM+rm5tPQpuCX+FPwixDu3y/MzmBxEpzYjagry2d3e2/QZcgspOAXAV7e18mq2iLS0pJn6GRdeT77OvoZHQsFXYrMMgp+SXldAyO81tTNmYtKgy7lderK8hkZc5qzR+JOwS8p74XdHTgHZ9cl1+LmkTUBdrSqu0fiS8EvKW/d7kNkZaSxZkFx0KW8zine1BHbW3oCrkRmGwW/pLx1uzs4vbaYnMzEL65+IgXZGdSU5LK1WcEv8aXgl5TW1T/CpsYu3lSXXP37ESsqC9nWPNkieCKxU/BLSnt6RxshB28/ZV7QpUxqeUUhDW19DI9qZI/Ej4JfUtpTW1spycvk9CS5cGuiUyoLGQ05drXpBK/Ej4JfUtZYyPHU9jbevryc9CQavz/eisrwFNHb1M8vcaTgl5S14UAnHX3DnLciObt5IDw9c2a6sU0jeySOFPySstZuaSXN4G3LyoMu5bgy09NYUl7A1iad4JX4UfBLSnLO8ciGg7x5yVxK8rOCLueEVlYXsbGxC+dc0KXILKHgl5S0sbGLPYf6ec/q6qBLOanTa4to7x2msVNTN0h8KPglJT386kEy041LVlYFXcpJrfLWCNhwoCvYQmTWUPBLygmFHI9saOLty8spyssMupyTWlFVSFZ6Gq8e6Ay6FJklFPyScp7Z0UZT1yBXnD4/6FKikp2RzqlVhWzYrxa/xIeCX1LOj9btY25+FhevrAy6lKitri1mw4FOzc0vcaHgl5TS0j3I2q2tfKC+lqyMmfP2P3NRKX3DY2w+qGGdMn0z550vEgf3Pb+PsZDjmrNqgy5lSs5eHJ5Ebt3uQwFXIrOBgl9SxsDwGD98bi/nr5jHwrnJs7ZuNOYV5rC4LJ91DR1BlyKzgIJfUsZPXthHR98wn3rHkqBLicnZi0t5fncHYyFdyCXTo+CXlDAyFuJ7z+6mfmEJ9Um2tm603rR4Lj1Do2xs1OgemR4Fv6SE+57fR2PnADecvzToUmL21mXlmMGTW1uDLkVmOAW/zHq9Q6N8e+0Ozq4r5R3Lk3dCtpMpzc9iTW0xv1PwyzT5Fvxm9gMzazWzTeO2lZrZ42a2w/te4tfxRSLufnoX7b3D3PyuFZgl57z70Tp/xTw2NnbR2j0YdCkyg/nZ4v8P4JIJ224G1jrnlgFrvfsivtnZ2st3n27gPaurWbNg5rczzl9RAcBatfplGnwLfufcM8DEsWdXAPd6t+8FrvTr+CLOOb7wi43kZKbxD5edFnQ5cXFqVSF1Zfk8/OrBoEuRGSzRffwVzrkm73YzUHG8Hc3sejNbb2br29raElOdzCrffbqBdbs7uOXdp1JemB10OXFhZly+uprnGg7Rou4eiVFgJ3ddeFWJ4w5Ids7d7Zyrd87Vl5fP3BNyEozndh3ijt9s5dJVVVx95sy6Svdk3rO6GudQq19ilujgbzGzKgDvuzoqJe5augf5n/e9RF1ZPl+5atWMP6E70dJ5BayqKeKn6/drVS6JSaKD/yHgOu/2dcCDCT6+zHIjYyE+/aOX6B8e47vXvpGC7IygS/LFtWcvZHtLL8/v1hQOMnV+Due8D3gOOMXMDpjZx4HbgYvMbAdwoXdfJG6++thWXthzmH953xtYVlEYdDm+uXx1NXNyMvivdfuCLkVmIN+aQ865a47z0AV+HVNS2683NvG9Z3dz3ZsXzphFVmKVm5XOB+pr+eFze2jpPpWKOTlBlyQziK7clVmhoa2Xz96/gdNri/nCpbNj6ObJfOScRYQc3PV0Q9ClyAyj4JcZb3BkjE/990tkphvf+dAZM2qBlemoLc3jytPn86Pn99LeOxR0OTKDpMb/EJnVvvzwa2xt7uGbV6+hujg36HIS6lPnLWFoNMQ9z+4OuhSZQRT8MqM99OpB7nt+H596xxLePoMnYIvVkvICLltVzQ+f20Nbj1r9Eh0Fv8xYe9r7+PwDG3njwhJuumh50OUE5qaLljM8GuKbT2wPuhSZIRT8MiMNjY7x6fteIj3N+PY1a8hIT923cl1ZPh86ewE/fmE/O1t7gy5HZoDU/d8iM9rXf7udTY3d3PH+VcxPsX79yfyvC5aRl5nO7b/eGnQpMgMo+GXGeXZHG3c/08CH37SQd66sDLqcpDC3IJtPnreEJ7a08Mx2TWooJ6bglxnlUO8QN/30VZbNK+ALl54adDlJ5WPn1lFXls+XHtzE4MhY0OVIElPwy4zhnOOz92+ga2CEb1+zhpzM9KBLSio5men84xUr2XOon7uf0UVdcnwKfpkx7nl2N7/b2srn37WCU6vmBF1OUnrrsnIuW1XF/31yJ/sO9QddjiQpBb/MCL/f0c6//HoL7/qzSq47Z1HQ5SS1f7jsNDLT07j5gQ2EQpq2WY6l4Jekt6utl0/f9xJL5xXwtQ+snnXz68dbxZwcvnjpqfxx1yF++NyeoMuRJKTgl6TW2DnAh+9ZR0aacfeH68mfpfPrx9sHz6zlvFPKuf2xrTS0aWy/vJ6CX5LW/o5+rr1nHT1Do9z7sbNYVJYfdEkzhplx+1WryM5I59M/epmBYY3ykaMU/JKUNjV28d7v/JFDvUP8x0fPZGV1UdAlzTgVc3L45gdPZ0tzN7c8sEHLNMoRCn5JKs45/vNPe7nq//2RrHTj5588hzcuLA26rBnrvBXz+NuLlvPLVw7yb7/bGXQ5kiTUYSpJ42DnAF96cDNPbGnh7cvL+doHVlNemB10WTPeDectpaGtj68/vp3crHT+6q2Lgy5JAqbgl8ANj4b4wR928+21OxgLOb546al87Nw60tI0eicezIyvvn8Vg6Nj3ParLbT1DPG5S1bo55vCFPwSmLGQ46FXG/nWEzvYc6ifC0+t4H9ffhq1pXlBlzbrZKSn8e2r11CSt5m7nmlg88Fu7vjAKqqKNMFdKlLwS8KFQo5HNzVx5+Pb2dXWx6lVc/jBR+o5f0VF0KXNahnpadx25Z+xsrqIf3rkNS6+8xk+e8kKrjmzNqWntU5FNhPO9NfX17v169cHXYZMk3OO377Wwp2Pb2drcw/L5hXwmYuWc8nKSnU7JNie9j5ufmADf2ro4JSKQv7hstN4y7KyoMuSODOzF51z9cdsV/CL35xz/H5nO3f8ZhsbDnRRV5bP31y4jMtWVZOuwA+Mc47HNjXzfx7dwoHDA5y/Yh43v2sFyysKgy5N4kTBL4HY3tLDlx7cxJ8aOphfnMuNFyzjfWfMV9dCEhkcGePf/7CH7zy1k76hUf68vpbPXLScijk5QZcm06Tgl4QaHg3x3ad38a+/20FBdgY3XrCMa85eQHaGplJOVof7hvm3J3fyw+f2kJ5mfOKti7n+bYspzMkMujSJkYJfEmbDgU7+/v4NbG3u4fLV1dx6+WnMLdB4/Jli36F+7vjtNh5+9SBz87O48cJlXHPWAjL1V9qMo+AX3w2OjHHnE9v53jMNlBdmc9uVb+Ci0zRSZ6Z6dX8n//zoFtbt7mDR3Dw+UF/L25aVs6yiQIvgzBAKfvHVH3a288VfbmJ3ex9Xn1nLLe8+laJcdRHMdM45ntzWyr/+bicv7+sEwAzyszLIzUonzcAwzMDgyJTZRbmZvGF+EWcvLuWCFRUU5em9EAQFv/hi76E+vvH4dh585SAL5+bxz+99A+cu1bDA2ai5a5AX9x5mR2sP3QOjDIyMEgqBw+EcOPC+O9p6htjY2EVn/wgZacY5S8t475pq3nlapabWTiAFv8RNz+AIf2ro4MFXGnl0YxMZ6Wn89dsW86nzlqoLQI4IhRwbGrv49aYmHnm1icbOAXIz07l4ZQVXrpnPW5aWaXSXz5Iq+M3sEuBbQDpwj3Pu9hPtr+D3h3OOlu4hdrX1squtl52tvRzsHKBvaIz+kTFGx0KMhdzRL+cYHg3R1DUIhP+c//P6Gj7x1sXM09A/OYFQyPHivsP84uVGfrWhia6BEcoKsrhsVTXvXTOfVTVFWlnNB0kT/GaWDmwHLgIOAC8A1zjnXjvecxT8sQmFHD1Do3T1j9DeN8S+Q/3sPdTP3kN9Xtj30Ts0emT/guwMakpyKczJICczneyMNNLMyEg30tPSyEgz0tOMBaV5rFlQzJsWz9VID5myodExntrWxi9fbmTt1laGR0NH3lNvmF9EXVk+1cW5VBXlUJCdob8KpuF4wR9EZ9tZwE7nXAOAmf0YuAI4bvDH6gu/2Mi63R1HFqB43Uec45htE/cb/5novK2RbZN9Xk52nCP7T3j+5Mc5+qCban0Tj+2gb3iUydbarirKYUl5AVedMZ8l8wpYWl7AknkFzCvMVqtLfJedkc7FKyu5eGUlXQMjPLapicdfa2VdQwcPvnLwmP2zMtLIz0onJzOdNPNOJBukmR29D7P2vfuD685kwdz4TlwYRPDPB/aPu38AOHviTmZ2PXA9wIIFC2I6UHVxLqdELj+3132LHGOSba/fb/ybySbcsHHPPPZ5417T23pkn9e9P22S/Se+5omOc+ybPbKpIDuDotxMivOyKMnLZEFpHrWleeqHl6RRlJvJB89cwAfPDP8fb+8dYl9HP02dgzR3D9I3NErf8Cj9Q2MMjozhgJDzTiY7R8gdvT9bZWXE/y+epD297py7G7gbwl09sbzGDectjWtNIuKvsoJsygqyIba2nkQpiM6zRqB23P0ab5uIiCRAEMH/ArDMzOrMLAu4GngogDpERFJSwrt6nHOjZvZp4DeEh3P+wDm3OdF1iIikqkD6+J1zjwKPBnFsEZFUpwGyIiIpRsEvIpJiFPwiIilGwS8ikmJmxOycZtYG7I3jS5YB7XF8vXhRXdFLxpogOetKxpogOetKxpog9roWOufKJ26cEcEfb2a2frKJi4KmuqKXjDVBctaVjDVBctaVjDVB/OtSV4+ISIpR8IuIpJhUDf67gy7gOFRX9JKxJkjOupKxJkjOupKxJohzXSnZxy8ikspStcUvIpKyFPwiIilm1ga/mZWa2eNmtsP7XnKc/a7z9tlhZteN236NmW00sw1m9piZlSVJXVlmdreZbTezrWZ2VdA1jXv8ITPbNN164lGXmeWZ2a+8n9FmM7t9mrVcYmbbzGynmd08yePZZvYT7/F1ZrZo3GO3eNu3mdnF06kjXnWZ2UVm9qL3Hn/RzM4PuqZxjy8ws14z+7t41TTdusxslZk9572XNppZTtB1mVmmmd3r1bPFzG6J+qDOuVn5BXwVuNm7fTPwlUn2KQUavO8l3u0SwrOWtgJl417r1qDr8h77MnCbdzstUmOQNXmPvw/4EbApSX6HecB53j5ZwLPAu2KsIx3YBSz2XutV4LQJ+3wK+K53+2rgJ97t07z9s4E673XS4/TzmU5da4Bq7/afAY1B1zTu8fuBnwF/F8f30nR+VhnABmC1d39ukvwO/wL4sXc7D9gDLIrquPH6wSbbF7ANqPJuVwHbJtnnGuCucffv8rZlAm3AQsLL234XuD7ourzb+4H8ZPlZebcLgN8TDrl4Bv+06pqw37eAT8RYx5uB34y7fwtwy4R9fgO82budQfgqS5u47/j94vDzibmuCfsY0AFkB10TcCVwB3Ar8Q3+6fwO3w38V7xqiWNd1wAPe9vmAtuB0miOO2u7eoAK51yTd7sZqJhkn8kWfp/vnBsBPglsBA4SDrTvB12XmRV79//JzF4ys5+Z2WTPT1hNkXqArwP9caglnnUB4P3cLgfWxljHSY8xfh/n3CjQRfg/YzTPjdV06hrvKuAl59xQkDWZWQHwOcJ/1cbbdH5WywFnZr/x/t/9fZLUdT/QBzQB+4CvOec6ojlo0i62Hg0zewKonOShL4y/45xzZhb1uFUzyyQc/GsIdx38K+FP4tuCrIvw76sG+KNz7iYzuwn4GvDhoGoys9OBJc65z0zsq43y+X79rCKvnwHcB3zbOdcw1efPdma2EvgK8M6gayHcyr/TOddrZkHXMl4G8BbgTMKNm7Vm9qJzLtaGRLycBYwB1YS7N581syeieZ/P6OB3zl14vMfMrMXMqpxzTWZWRbjPfqJG4B3j7tcATwGne6+/y3utnxLuYw66rkOE33gPeNt/Bnw84JreDNSb2R7C76d5ZvaUc+4dRMHHuiLuBnY4574ZTT3H0QjUTjhG43H2OeB92BQR/n1F89wg6sLMaoBfAH8Zea8HXNPZwPvN7KtAMRAys0Hn3L8FXNcB4BnnXDuAmT0KnEHsf0HGq66/AB7zeihazewPQD3hxuqJ+dFvlQxfhPsJx58Y/Ook+5QCuwl/WpZ4t0sJf4I2AeXefv8EfD3ourzHfgyc793+CPCzoGsat88i4tvHP92f1W3Az4G0adaR4f1nquPoCbiVE/a5gdefgPupd3slrz+520D8TgxOp65ib//3xev3Nd2aJuxzK/Ht45/Oz6oEeInwCdQM4Ang0iSo63PAv3u384HXgFVRHTeev/Rk+iLcB7YW2OH9oiJhUA/cM26/jwE7va+Pjtv+18AWwmfzHwbmJkldC4FnvLrWAguCrmnc44uIb/DHXBfhlpPzfoeveF9/NY1a3k345Nku4Avetn8E3uPdziH8F9hO4Hlg8bjnfsF73jZiHFkU77qALxLuH35l3Ne8IGua8Bq3Esfgj8Pv8FpgM7CJSRogAf0OC7ztmwmH/mejPaambBARSTGzeVSPiIhMQsEvIpJiFPwiIilGwS8ikmIU/CIiKUbBLyKSYhT8IiIp5v8DQLdKcXnPAIAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Volatility-weighted Historical Simulation\n",
    "# 道琼斯指数收益率500样本分布\n",
    "r.plot.kde()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    500.000000\n",
       "mean       0.000026\n",
       "std        0.011088\n",
       "min       -0.042323\n",
       "25%       -0.004113\n",
       "50%        0.000626\n",
       "75%        0.005384\n",
       "max        0.038647\n",
       "Name: DJIA, dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Day'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Volatility-weighted Historical Simulation:\n",
      "95% VaR = 461.9683\n"
     ]
    }
   ],
   "source": [
    "# EWMA Model\n",
    "l = 0.94\n",
    "x = pd.Series(np.zeros(n+1))\n",
    "x[1:] = r**2\n",
    "x[0] = r.var()\n",
    "y = x.ewm(alpha=1-l, adjust=False).mean()\n",
    "yT = l * y.loc[n] + (1-l) * r.loc[n]**2\n",
    "r_new = np.sqrt(yT/y)*r\n",
    "profit_new = r_new * djia\n",
    "VaR95 = -profit_new.quantile(q=0.05,interpolation='higher')\n",
    "print(\"Volatility-weighted Historical Simulation:\")\n",
    "print('95% VaR =', np.around(VaR95,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# EWMA模型预测的波动率走势图\n",
    "np.sqrt(y).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 参数法\n",
    "假定资产的P/L服从某个分布，用样本估计总体的参数，然后根据分布的分位点来计算。\n",
    "对于正态分布，alpha置信水平下的VaR为：\n",
    "\n",
    "$$\n",
    "\\alpha VaR =-\\mu_{P/L}+\\sigma_{P/L}z_{\\alpha} \n",
    "$$\n",
    "\n",
    "#### 极值理论\n",
    "1. 两种方法\n",
    "* GEV\n",
    "    * Frechet分\n",
    "    * Gumbel\n",
    "    * Willbul\n",
    "* POT\n",
    "2. 实际运用中的一些考量\n",
    "* 根据场景上下文和数据可得性\n",
    "* GEV可能损失一些极值数据\n",
    "* POT的threshold选取问题\n",
    "3. 方法改进\n",
    "* Conditional EV\n",
    "* Dealing with dependent (or non-iid) data\n",
    "* Multivariate EVT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05   -1.097189\n",
       "0.95    2.970195\n",
       "dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example 1 \n",
    "# Gumbel quantiles\n",
    "# For the standardised Gumbel, the 5% and 95% quantiles are\n",
    "def gumble_quantile(q, mu, sigma):\n",
    "    return pd.Series(mu - sigma*np.log(-np.log(q)), index=q)\n",
    "gumble_quantile(q=[0.05, 0.95], mu=0, sigma=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05   -0.985149\n",
       "0.95    4.056448\n",
       "dtype: float64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example 2 \n",
    "# Frechet quantiles\n",
    "# For the standardised Frechet with ki=0.2, the 5% and 95% quantiles are\n",
    "def frechet_quantile(q, mu, sigma, ki):\n",
    "    return pd.Series(mu - sigma*(1 - np.power(-np.log(q), -ki))/ki, index=q)\n",
    "frechet_quantile(q=[0.05, 0.95], mu=0, sigma=1, ki=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05   -0.934899\n",
       "0.95    4.792363\n",
       "dtype: float64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For ki=0.3\n",
    "frechet_quantile(q=[0.05, 0.95], mu=0, sigma=1, ki=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.605770    0.690642\n",
       "0.904792    2.302085\n",
       "dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example 3\n",
    "# Gumbel VaR\n",
    "# For the standardisd Gumbel and n=100, the 99.5% and 99.9% VaRs are\n",
    "n = 100\n",
    "gumble_quantile(q=np.power([.995, .999], n), mu=0, sigma=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.605770    0.740615\n",
       "0.904792    2.923673\n",
       "dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example 4\n",
    "# Frechet VaR\n",
    "# For standardised Frechet with ki=0.2 and n=100, the 99.5% and 99.9% VaRs are\n",
    "n = 100\n",
    "frechet_quantile(q=np.power([.995, .999], n), mu=0, sigma=1, ki=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.605770    0.767398\n",
       "0.904792    3.316543\n",
       "dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For ki=0.3, the 99.5% and 99.9% VaRs are\n",
    "frechet_quantile(q=np.power([.995, .999], n), mu=0, sigma=1, ki=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.952214702690108"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example 5\n",
    "# POT risk measures\n",
    "# Suppose setting the parameters of POT at empirically plausible values denominated in % term\n",
    "# beta=0.8, ki=0.15, u=2% and N/n=4%\n",
    "# The 99.5% VaR (in %) is\n",
    "def pot_VaR(alpha, u, beta, ki, ratio):\n",
    "    return u + beta*(np.power((1/ratio)*(1-alpha), -ki) - 1)/ki\n",
    "pot_VaR(.995, 2, .8, .15, .04)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.237899650223656"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The corresponding ES (in %) is\n",
    "def pot_ES(alpha, u, beta, ki, ratio):\n",
    "    VaR = pot_VaR(alpha, u, beta, ki, ratio)\n",
    "    return VaR/(1-ki) + (beta-ki*u)/(1-ki)\n",
    "pot_ES(.995, 2, .8, .15, .04)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Backtesing\n",
    "回测是为了检验模型的正确与否。涉及到三个方面：\n",
    "* 使用哪个收益\n",
    "* Failure Rate的二项检验\n",
    "* 巴塞尔协议的相关规定"
   ]
  }
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